Academic Worksheet 9.1
Find the square roots of the number.
1. 36
2. 4900
3. 10,000
4. 169
Approximate the square root to the nearest integer.
5. √39
6. √105
7. −√3.3
Use a calculator to approximate the square root. Round to the nearest tenth.
8. √102
9. −√74
10. √1585
Evaluate the expression when 𝑎 = 72 and 𝑏 = 8.
11. √𝑎 − 𝑏
12. √𝑎 + 𝑏 + 1
Solve the equation. Round to the nearest tenth if necessary.
14. 𝑥 2 = 64
15. 225 = 𝑛2
13. −4√𝑎𝑏
16. 7𝑦 2 = 63
Solve the equation. Round to the nearest hundredth if necessary.
17. 2𝑥 2 = 32
18. 5𝑦 2 − 4 = 74
19. Write an equation that has exactly two solutions: 9 and − 9.
20. A square ice skating rink has an area of 1849 square feet. What is the perimeter of the rink?
21. A forest ranger is stationed in a 58 foot tall fire tower. The equation for the distance in miles
that the ranger can see is 𝑑 = √1.5ℎ, where ℎ is the height in feet above the ground. Find the
distance the ranger can see. Round your answer to the nearest tenth.
Academic Worksheet 9.3 – Day 1
Find the unknown length. Round your answer to the nearest tenth.
1.
2.
3.
Determine whether the triangle with the given side lengths is a right triangle.
4. 3, 5, 6
5. 7, 11, 13
6. 10, 50, 51
The lengths of two sides of a right triangle are given. Find the length of the third side.
7. 𝑎 = 9, 𝑐 = 41
8. 𝑎 = 28, 𝑏 = 45
9. 𝑏 = 9, 𝑐 = 15
10. A ladder that is 12 feet long is placed against a wall. The bottom of
the ladder is 4 feet from the wall. To the nearest foot, how far up the
wall does the ladder reach?
a. Label the know lengths. Label the unknown length 𝑥.
b. Use the Pythagoream theorem to write an equation you can
use to find the value of 𝑥.
c. Solve the equation in part (b) for 𝑥.
d. Round your answer from part (c) to the nearest whole
number.
11. A sheet of paper is 8.5 inches by 11 inches. How long is the diagonal of the paper? Round your
answer to the nearest tenth of an inch.
Academic Worksheet 9.3 – Day 2
Find the unknown length. Round your answer to the nearest tenth.
1.
2.
3.
Determine whether the triangle with the given side lengths is a right triangle.
4. 8, 15, 17
5. 9, 12, 15
6. 11, 13, 17
The lengths of two sides of a right triangle are given. Find the length of the third side.
7. 𝑎 = 40, 𝑐 = 58
8. 𝑎 = 13, 𝑏 = 84
9. 𝑏 = 70, 𝑐 = 74
10. A support wire 12 yards long is attached to the top of a utility
pole 10 yards tall and is then stretched taut. To the nearest
tenth of a yard, find how far from the base of the pole the wire
will be attached to the ground.
11. An access ramp has a height of 5 feet and a horizontal distance of 60 feet. Find the length 𝑙 of
the ramp to the nearest tenth of a foot.
Academic Worksheet 9.4
Tell whether the number is rational or irrational.
1.
1
7
̅̅̅̅
3. 1. 12
1
2. √7
5. −9.61
6.
√5
16
81
7. √25
4. −√17
8. −
√16
5
Complete the statement using >, <, or =.
1
1
11. −√8_____ −
32
9. √4 _____ 4
10. 4_____√ 2
10
3
12. Order the numbers from least to greatest.
4.2, √17,
17 81
,√
4
5
13. One leg of a right triangle is 6 inches long. The other leg is 8 inches long. Is the length in inches
of the hypotenuse a rational or irrational number?
14. You made a cardboard tree that is 48 inches tall to use as
a stage prop for a play. You need to make a diagonal
brace that connects a 28-inch long horizontal brace to
the top of the tree. Find the length of the diagonal brace
to the nearest tenth of an inch.
15. You want to buy some frozen pizzas that have a diameter of 18 inches. You need to be able to
fit them into your upright freezer that has a capacity of 4.5 cubic feet. The storage
compartment of the freezer is 2 feet high. The width and depth of the compartment can be
4.5
found using the expression √ 2 . Will the pizzas lay flat on the shelves of your freezer? Explain.